System and method for feature selection in decision trees

ABSTRACT

Selection of certain attributes as output and input attributes is provided so a decision tree may be created more efficiently. For each possible output attribute an interestingness score is calculated. This interestingness score is based on entropy of the output attribute and a desirable entropy constant. The attributes with the highest interestingness score are used as output attributes in the creation of the decision tree. Score gains for the input attribute over the output attributes are calculated using a conventional scoring algorithm. The sum of the score gains over all output attributes for each input attribute is calculated. The attributes with the highest score gain sums are used as input attributes in the creation of the decision tree.

FIELD OF THE INVENTION

The present invention relates to systems and methods for selectingfeatures to use either input attributes or output attributes in traininga decision tree. More specifically, the present invention relates to amaximum interestingness score for calculating the relative usefulness offeatures as output attributes to a decision tree. The present inventionalso relates to a maximum split score for calculating the relativeusefulness of features as input attributes to a decision tree.

BACKGROUND OF THE INVENTION

Data mining is the exploration and analysis of large quantities of data,in order to discover correlations, patterns, and trends in the data.Data mining may also be used to create models that can be used topredict future data or classify existing data.

For example, a business may amass a large collection of informationabout its customers. This information may include purchasing informationand any other information available to the business about the customer.The predictions of a model associated with customer data may be used,for example, to control customer attrition, to perform credit-riskmanagement, to detect fraud, or to make decisions on marketing.

To create and test a data mining model such as a decision tree,available data may be divided into two parts. One part, the trainingdata set, may be used to create models. The rest of the data, thetesting data set, may be used to test the model, and thereby determinethe performance of the model in making predictions. Data within datasets is grouped into cases. For example, with customer data, each casecorresponds to a different customer. All data in the case describes oris otherwise associated with that customer.

One type of predictive model is the decision tree. Decision trees areused to classify cases with specified input attributes in terms of anoutput attribute. Once a decision tree is created, it can be usedpredict the output attribute of a given case based on the inputattributes of that case.

Decisions trees are composed of nodes and leaves. One node is the rootnode. Each node has an associated attribute test that splits cases thatreach that node to one of the children of the node based on an inputattribute. The tree can be used to predict a new case by starting at theroot node and tracing a path down the tree to a leaf, using the inputattributes of the new case in the attribute tests in each node. The pathtaken by a case corresponds to a conjunction of attribute tests in thenodes. The leaf contains the decision tree's prediction for the outputattribute(s) based on the input attributes.

An exemplary decision tree is shown in FIG. 1. In this decision tree, orexample, if a decision tree is being used to predict a customer's creditrisk, input attributes may include debt level, employment, and age, andthe output attribute is a prediction of what the credit risk for thecustomer is. As shown in FIG. 1, decision tree 200 consists of root node210, node 212, and leaves 220, 222 and 224. The input attributes aredebt level and type of employment, and the output attribute is creditrisk. Each node has associated with it a split constraint based on oneof the input attributes. For example, the split constraint of root node210 is whether debt level is high or low. Cases where the value of thedebt input attribute is “high” will be transferred to leaf 224 and allother cases will be transferred to node 212. Because leaf 224 is a leaf,it gives the prediction the decision tree model will give if a casereaches leaf 224. For decision tree 200, all cases with a “high” valuefor the debt input attribute will have credit risk output attributeassigned to “bad” with a 100% probability. The decision tree 200 in FIG.1 predicts only one output attribute, however more than one outputattribute may be predicted with a single decision tree.

While the decision tree may be displayed and stored in a decision treedata structure, it may also be stored in other ways, for example, as aset of rules, one for each leaf node, containing a conjunction of theattribute tests.

Input attributes and output attributes do not have to be binaryattributes, with two possible states. Attributes can have many states.In some decision tree creation contexts, attribute tests must be binary.Binary attribute tests divide data into two groups—one group of datathat meets a specific test, and one group of data that does not.Therefore for an attribute with many states (e.g. a color variable withpossible states {red, green, blue, violet}) a binary attribute test mustbe based on the selection of one of the states. Such an attribute testmay therefore ask whether, for input attribute color, is the value ofthat attribute the state “red” and data at the node will be split intodata for which the value of the attribute is “red” in one child, anddata for which the value of the attribute is not “red” in another child.

In order to create the tree, the nodes, attribute tests, and leaf valuesmust be decided upon. Generally, creating a tree is an inductiveprocess. Given an existing tree, all testing data is processed by thetree, starting with the root node, divided according to the attributetest to nodes below, until a leaf is reached. The data at each leaf isthen examined to determine whether and how a split should be performed,creating a node with an attribute test leading to two leaf nodes inplace of the leaf node. This is done until the data at each node issufficiently homogenous. In order to begin the induction the root nodeis treated as a leaf.

To determine whether a split should be performed, a score gain iscalculated for each possible attribute test that might be assigned tothe node. This score gain corresponds to the usefulness of using thatattribute test to split the data at that node. There are many ways todetermine which attribute test to use using the score gain. For example,the decision tree may be built by using the attribute test that reducesthe amount of entropy at the node. Entropy is a measure of thehomogeneity of the data. The data at the node must be split into twogroups of data which each are heterogeneous from each other based on theoutput attribute for which the tree is being generated.

In order to determine what the usefulness is of splitting the data atthe node with a specific attribute test, the resultant split of the dataat the node for each output attribute must be computed. This correlationdata is used to determine a score which is used to select an attributetest for the node. Where the input attribute being considered is gender,for example, and the output attribute is car color, the data from thefollowing Table 1 must be computed for the testing data that reaches thenode being split:

TABLE 1 Correlation Count Table gender = MALE gender ≠ MALE car color =RED 359 503 car color ≠ RED 4903 3210

As described above, data in a correlation count table such as that shownin Table 1 must be calculated for each combination of a possible inputattribute test and output attribute description. Because of themultiplicity of correlation count table calculations required, the moreattributes considered, the higher the requirements in memory space andprocessing time to calculate these correlation count tables. One way ofhandling this problem is to select certain features to be used for inputand output attributes. In the prior art, where this is done at all, itis done by selecting the input attributes with highest entropy for usein the decision tree. However, this yields poor results in terms ofquality of prediction. Output attribute selection was only done by useof a user-supplied hierarchy, which yields no definite predictionquality gains and, indeed, often creates a worse prediction quality,since grouping attributes with different behavior negatively affectsdecision tree quality.

Thus, there is a need for a technique to allow the selection of outputattributes and input attributes in such a way as to narrow the number ofattributes used in training the decision tree while simultaneouslyselecting attributes for use which yield efficient and useful decisiontrees.

SUMMARY OF THE INVENTION

In view of the foregoing, the present invention provides systems andmethods for using selecting input attributes and output attributes foruse in training a decision tree. Output attributes are chosen based on amaximum interestingness score method, where the interestingness score isbased on the entropy of the attribute and a most favored interestingnessscore. A predetermined number of attributes with the highestinterestingness scores are selected for use in decision tree training.In another embodiment all output attributes with interestingness scoresabove a certain level are selected for use in decision tree training.

Input attributes are chosen by calculating score gain sums for eachinput attribute. This score gain is based on the split scores and nodescores of the input and output attributes. A predetermined number ofinput attributes with the highest score gain sum are selected for use indecision tree training. In another embodiment, all input attributes withscore gain sums above a certain level are selected for use in decisiontree training.

BRIEF DESCRIPTION OF THE DRAWINGS

The system and methods for selecting input and output attributes indecision trees in accordance with the present invention are furtherdescribed with reference to the accompanying drawings in which:

FIG. 1 is a block diagram depicting an exemplary decision tree.

FIG. 2 is a block diagram of an exemplary computing environment in whichaspects of the invention may be implemented.

FIG. 3 is a graph of the interestingness scores of data sets withmaximum entropy over an attribute with a certain number of statesaccording to one embodiment of the present invention.

FIG. 4 is a block diagram of the technique for selection of input andoutput attributes according to the invention.

FIG. 5 is a block diagram of a system according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

Overview

As described in the background, the selection of input attributes foruse in decision tree creation from the set of all possible inputattributes and the selection of output attributes for use in decisiontree creation from the set of all possible output attributes, when it isdone, is often haphazard or done in a way which does not maximize theutility of the resulting decision tree.

In order to select output attributes for use in decision tree creation,an “interestingness” score is calculated for each possible outputattribute, and the attributes selected are those with the highestinterestingness scores. In order to select input attributes for use indecision tree creation, a score gain sum is calculated for each possibleinput attribute (taking into account the output attributes) and theattributes selected are those with the highest score gain sums.

As output attribute selection is independent of input attributes, theoutput attribute selection is performed first in one embodiment of theinvention. Because input attribute selection is dependent on outputattributes, the reduced number of output attributes will result inincreased space and processing time efficiency.

Exemplary Computing Environment

FIG. 2 illustrates an example of a suitable computing system environment100 in which the invention may be implemented. The computing systemenvironment 100 is only one example of a suitable computing environmentand is not intended to suggest any limitation as to the scope of use orfunctionality of the invention. Neither should the computing environment100 be interpreted as having any dependency or requirement relating toany one or combination of components illustrated in the exemplaryoperating environment 100.

One of ordinary skill in the art can appreciate that a computer or otherclient or server device can be deployed as part of a computer network,or in a distributed computing environment. In this regard, the presentinvention pertains to any computer system having any number of memory orstorage units, and any number of applications and processes occurringacross any number of storage units or volumes, which may be used inconnection with the present invention. The present invention may applyto an environment with server computers and client computers deployed ina network environment or distributed computing environment, havingremote or local storage. The present invention may also be applied tostandalone computing devices, having programming language functionality,interpretation and execution capabilities for generating, receiving andtransmitting information in connection with remote or local services.

The invention is operational with numerous other general purpose orspecial purpose computing system environments or configurations.Examples of well known computing systems, environments, and/orconfigurations that may be suitable for use with the invention include,but are not limited to, personal computers, server computers, hand-heldor laptop devices, multiprocessor systems, microprocessor-based systems,set top boxes, programmable consumer electronics, network PCs,minicomputers, mainframe computers, distributed computing environmentsthat include any of the above systems or devices, and the like.

The invention may be described in the general context ofcomputer-executable instructions, such as program modules, beingexecuted by a computer. Generally, program modules include routines,programs, objects, components, data structures, etc. that performparticular tasks or implement particular abstract data types. Theinvention may also be practiced in distributed computing environmentswhere tasks are performed by remote processing devices that are linkedthrough a communications network or other data transmission medium. In adistributed computing environment, program modules and other data may belocated in both local and remote computer storage media including memorystorage devices. Distributed computing facilitates sharing of computerresources and services by direct exchange between computing devices andsystems. These resources and services include the exchange ofinformation, cache storage, and disk storage for files. Distributedcomputing takes advantage of network connectivity, allowing clients toleverage their collective power to benefit the entire enterprise. Inthis regard, a variety of devices may have applications, objects orresources that may utilize the techniques of the present invention.

With reference to FIG. 2, an exemplary system for implementing theinvention includes a general-purpose computing device in the form of acomputer 110. Components of computer 110 may include, but are notlimited to, a processing unit 120, a system memory 130, and a system bus121 that couples various system components including the system memoryto the processing unit 120. The system bus 121 may be any of severaltypes of bus structures including a memory bus or memory controller, aperipheral bus, and a local bus using any of a variety of busarchitectures. By way of example, and not limitation, such architecturesinclude Industry Standard Architecture (ISA) bus, Micro ChannelArchitecture (MCA) bus, Enhanced ISA (EISA) bus, Video ElectronicsStandards Association (VESA) local bus, and Peripheral ComponentInterconnect (PCI) bus (also known as Mezzanine bus).

Computer 110 typically includes a variety of computer readable media.Computer readable media can be any available media that can be accessedby computer 110 and includes both volatile and nonvolatile media,removable and non-removable media. By way of example, and notlimitation, computer readable media may comprise computer storage mediaand communication media. Computer storage media includes both volatileand nonvolatile, removable and non-removable media implemented in anymethod or technology for storage of information such as computerreadable instructions, data structures, program modules or other data.Computer storage media includes, but is not limited to, RAM, ROM,EEPROM, flash memory or other memory technology, CDROM, digitalversatile disks (DVD) or other optical disk storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other medium that can be used to store the desired informationand that can accessed by computer 110. Communication media typicallyembodies computer readable instructions, data structures, programmodules or other data in a modulated data signal such as a carrier waveor other transport mechanism and includes any information deliverymedia. The term “modulated data signal” means a signal that has one ormore of its characteristics set or changed in such a manner as to encodeinformation in the signal. By way of example, and not limitation,communication media includes wired media such as a wired network ordirect-wired connection, and wireless media such as acoustic, RF,infrared and other wireless media. Combinations of any of the aboveshould also be included within the scope of computer readable media.

The system memory 130 includes computer storage media in the form ofvolatile and/or nonvolatile memory such as read only memory (ROM) 131and random access memory (RAM) 132. A basic input/output system 133(BIOS), containing the basic routines that help to transfer informationbetween elements within computer 110, such as during start-up, istypically stored in ROM 131. RAM 132 typically contains data and/orprogram modules that are immediately accessible to and/or presentlybeing operated on by processing unit 120. By way of example, and notlimitation, FIG. 2 illustrates operating system 134, applicationprograms 135, other program modules 136, and program data 137.

The computer 110 may also include other removable/non-removable,volatile/nonvolatile computer storage media. By way of example only,FIG. 2 illustrates a hard disk drive 140 that reads from or writes tonon-removable, nonvolatile magnetic media, a magnetic disk drive 151that reads from or writes to a removable, nonvolatile magnetic disk 152,and an optical disk drive 155 that reads from or writes to a removable,nonvolatile optical disk 156, such as a CD ROM or other optical media.Other removable/non-removable, volatile/nonvolatile computer storagemedia that can be used in the exemplary operating environment include,but are not limited to, magnetic tape cassettes, flash memory cards,digital versatile disks, digital video tape, solid state RAM, solidstate ROM, and the like. The hard disk drive 141 is typically connectedto the system bus 121 through an non-removable memory interface such asinterface 140, and magnetic disk drive 151 and optical disk drive 155are typically connected to the system bus 121 by a removable memoryinterface, such as interface 150.

The drives and their associated computer storage media discussed aboveand illustrated in FIG. 2, provide storage of computer readableinstructions, data structures, program modules and other data for thecomputer 110. In FIG. 2, for example, hard disk drive 141 is illustratedas storing operating system 144, application programs 145, other programmodules 146, and program data 147. Note that these components can eitherbe the same as or different from operating system 134, applicationprograms 135, other program modules 136, and program data 137. Operatingsystem 144, application programs 145, other program modules 146, andprogram data 147 are given different numbers here to illustrate that, ata minimum, they are different copies. A user may enter commands andinformation into the computer 20 through input devices such as akeyboard 162 and pointing device 161, commonly referred to as a mouse,trackball or touch pad. Other input devices (not shown) may include amicrophone, joystick, game pad, satellite dish, scanner, or the like.These and other input devices are often connected to the processing unit120 through a user input interface 160 that is coupled to the systembus, but may be connected by other interface and bus structures, such asa parallel port, game port or a universal serial bus (USB). A monitor191 or other type of display device is also connected to the system bus121 via an interface, such as a video interface 190. In addition to themonitor, computers may also include other peripheral output devices suchas speakers 197 and printer 196, which may be connected through anoutput peripheral interface 190.

The computer 110 may operate in a networked environment using logicalconnections to one or more remote computers, such as a remote computer180. The remote computer 180 may be a personal computer, a server, arouter, a network PC, a peer device or other common network node, andtypically includes many or all of the elements described above relativeto the computer 110, although only a memory storage device 181 has beenillustrated in FIG. 2. The logical connections depicted in FIG. 2include a local area network (LAN) 171 and a wide area network (WAN)173, but may also include other networks. Such networking environmentsare commonplace in offices, enterprise-wide computer networks, intranetsand the Internet.

When used in a LAN networking environment, the computer 110 is connectedto the LAN 171 through a network interface or adapter 170. When used ina WAN networking environment, the computer 110 typically includes amodem 172 or other means for establishing communications over the WAN173, such as the Internet. The modem 172, which may be internal orexternal, may be connected to the system bus 121 via the user inputinterface 160, or other appropriate mechanism. In a networkedenvironment, program modules depicted relative to the computer 110, orportions thereof, may be stored in the remote memory storage device. Byway of example, and not limitation, FIG. 2 illustrates remoteapplication programs 185 as residing on memory device 181. It will beappreciated that the network connections shown are exemplary and othermeans of establishing a communications link between the computers may beused.

Feature Selection of Output Attributes

The entropy of an attribute is a measure of the diversity of anattribute over a data set. To determine which attributes contain usefulinformation for use in a decision tree, the use of entropy has someappeal. High entropy for an output state has some desirability. If anattribute has low entropy, with many cases in the data set having thesame value for the attribute, then the homogeneity of data sets, evenafter splitting, may be high. This yields uninteresting predictions, andit is less likely that a split will uncover a useful distinction for alow entropy output attribute.

However, consider the case of an output attribute with 100,000 statescorresponding to the possible 5-digit zip codes. Although there arelikely to be many cases with certain of the most popular states, thereis also likely to be high entropy. Predicting such an output attribute,though, would yield a decision tree with many layers, likely one whichis inefficient to produce and inefficient to use.

The “interestingness” of an output attribute is a measure of how usefulthe attribute is in a decision tree. Two observations aboutinterestingness may be made. First, the more skewed the attribute, theless interesting the attribute will be. If all most all cases have acertain state as the value of the attribute, this is less interesting oruseful to predict. Second, the more diverse the attribute is, the lessthe attribute is interesting. Predicting customer phone numbers islikely to be costly in processing time and memory space, and likely toresult in low performance.

In one embodiment of the invention, in order to determine theinterestingness of an attribute, the entropy of the attribute should beconsidered as well as a most favored entropy value. The differencebetween the actual entropy and most favored entropy is used to determineinterestingness. In a preferred embodiment, the interestingness IS(A) ofan attribute A is given in equation (1):IS(A)=−(m−E(A))²  (1)where E(A) is the entropy of the attribute A, and where m is a mostfavored entropy value. Entropy may be calculated in a number of ways.One equation for entropy is given in equation (2):

$\begin{matrix}{{E(A)} = {\sum\limits_{i = 1}^{n}\left( {p_{i}*{\ln\left( p_{i} \right)}} \right)}} & (2)\end{matrix}$where p_(i) is the marginal probability of state i (of the n possiblestates) in attribute A in the data set being considered. This entropyequation is used in one embodiment of the invention, however it iscontemplated that any entropy equation may be used. In other words,p_(i) corresponds to the proportion of state i examples in the set. Themost favored entropy value m in equation (1) may be set before featureselection has begun, or it may be a parameter which can be setdynamically or by the user during the feature selection process. Onepossible value for m is the maximum entropy value for an attribute with10 states, that is, 1 n(10).

By using this interestingness score rather than entropy, both entropyand the number of states in the attribute are taken into account. InFIG. 3, a graph is provided which shows the interestingness scores(Y-axis) of attributes with maximum entropy (even distribution over allstates) for attributes with N states (X-axis). As can be seen from thisgraph, interestingness scores range between approximately −5.5 and 0,with an attribute with 10 states and maximum entropy scoring the maximumpossible score of 0.

When the interestingness score is created for each of possible outputattribute, according to one embodiment of the invention, the Kattributes with the highest interestingness scores are selected for usein the decision tree creation process. K may be set before featureselection has begun, or it may be a parameter that can be setdynamically or by the user during the feature selection process. In analternate embodiment of the invention, all attributes with aninterestingness score above a certain value are selected for use in thedecision tree creation process.

Feature Selection of Input Attributes

According to the present invention, selecting input attributes for usein creating a decision tree from among a set of possible inputattributes is done by calculating a gain score sum for each inputattribute. This gain score sum is based on the input attribute and alloutput attributes. On the other hand, as described, output attributeselection is independent of input attributes. Therefore, outputattributes should be selected first, to lower the number of outputattributes considered in input attribute selection and to prevent outputattributes which are not selected from influencing the calculation ofinput attributes.

A gain score G(O,I) for an input attribute I over an output attribute Ois calculated according to equation (3):G(O,I)=Splitscore(O,I)−Nodescore (O)  (3)where Splitscore (O,I) is the measure of the effect on output attributeO of a split over a data set based on input attribute I, and whereNodescore (O) is a measure of the score of a node before a split. Theentire training set is used to determine the Splitscore and theNodescore. Both Splitscore and Nodescore may be based on any scoringmeans. Existing scoring functions include Bayesian score and K2 score,but any scoring means which provides a score for a split and a node maybe used.

The score gain sum for an attribute I is the sum of the gain scores overall output attributes, as shown in equation (4):

$\begin{matrix}{\sum\limits_{j = 1}^{n}{G\left( {O_{j},I} \right)}} & (4)\end{matrix}$where O_(j) is the j-th output attribute of n total output attributes.This score gain sum will represent a measure of the effect of the inputattribute on the output attributes.

When the score gain sum is created for each of possible input attribute,according to one embodiment of the invention, the J attributes with thehighest score gain sum are selected for use in the decision treecreation process. J may be set before feature selection has begun, or itmay be a parameter that can be set dynamically or by the user during thefeature selection process. In an alternate embodiment of the invention,all attributes with a score gain sum above a certain value are selectedfor use in the decision tree creation process.

In an alternate embodiment of the invention, only a certain reducednumber of output attributes are used in calculating the score gain sumsfor the input attributes. This reduced number of output attributes maybe selected randomly, based on entropy, based on number of states, orbased on the interestingness score of the output attributes.

Feature Selection Process for Selecting Both Output and Input Attributes

As shown in FIG. 4, the feature selection process can be used for bothinput and output attributes. When this occurs, the interestingness scoreis calculated for each output attribute as shown in step 410. In oneembodiment, this is done according to the formula in equation (1) above.Next, at least one output attribute is selected for use in the decisiontree based on the interestingness scores 420.

Next, in step 430, a score gain sum is calculated for each inputattribute using the output attributes that had been selected in theprevious step. In one embodiment, this is done using the formula inequation (4) above. And, finally, in step 440, at least one inputattribute is selected for use in the decision tree based on the scoregain sums. In this way, the technique for the selection of outputattributes (steps 410 and 420 ) can be concatenated with the techniquefor the selection of input attributes (steps 430 and 440 ).

System For Selecting Output and Input Attributes

As shown in FIG. 5, the feature selection system includes a module forcalculating the interestingness score of output attributes 510, a modulefor selecting the output attributes for use 520, a module forcalculating a score gain sum is calculated for each input attribute 530,and a module for selecting input attributes 540. In a preferredembodiment, these modules are used with a control module 550 whichmanages the selection process.

CONCLUSION

Herein a system and method for selecting certain attributes as outputand input attributes in creating a decision tree. Limiting the number ofattributes used lessens memory space and processing time requirements.Selecting the attributes to use intelligently can lead to an increasedutility of the resulting tree over other possible reduced-attributedecision trees.

For each possible output attribute an interestingness score iscalculated. This interestingness score, based on entropy of the outputattribute and a desirable entropy constant, measures the possible inorder to avoid very diverse attributes which may have high entropy butare difficult to predict. The attributes with the highestinterestingness score are used as output attributes in the creation ofthe decision tree.

The invention also contemplates a technique for selecting inputattributes. Score gains for the input attribute over the outputattributes are calculated using a conventional scoring algorithm. Thesum of the score gains over all output attributes for each inputattribute is calculated. This score is a measure of the effect of theinput attribute on the output attributes. The attributes with thehighest score gain sums are used as input attributes in the creation ofthe decision tree.

As mentioned above, while exemplary embodiments of the present inventionhave been described in connection with various computing devices andnetwork architectures, the underlying concepts may be applied to anycomputing device or system in which it is desirable to create a decisiontree. Thus, the techniques for creating a decision tree in accordancewith the present invention may be applied to a variety of applicationsand devices. For instance, the algorithm(s) of the invention may beapplied to the operating system of a computing device, provided as aseparate object on the device, as part of another object, as adownloadable object from a server, as a “middle man” between a device orobject and the network, as a distributed object, etc. While exemplaryprogramming languages, names and examples are chosen herein asrepresentative of various choices, these languages, names and examplesare not intended to be limiting. One of ordinary skill in the art willappreciate that there are numerous ways of providing object code thatachieves the same, similar or equivalent parametrization achieved by theinvention.

The various techniques described herein may be implemented in connectionwith hardware or software or, where appropriate, with a combination ofboth. Thus, the methods and apparatus of the present invention, orcertain aspects or portions thereof, may take the form of program code(i.e., instructions) embodied in tangible media, such as floppydiskettes, CD-ROMs, hard drives, or any other machine-readable storagemedium, wherein, when the program code is loaded into and executed by amachine, such as a computer, the machine becomes an apparatus forpracticing the invention. In the case of program code execution onprogrammable computers, the computing device will generally include aprocessor, a storage medium readable by the processor (includingvolatile and non-volatile memory and/or storage elements), at least oneinput device, and at least one output device. One or more programs thatmay utilize the techniques of the present invention, e.g., through theuse of a data processing API or the like, are preferably implemented ina high level procedural or object oriented programming language tocommunicate with a computer system. However, the program(s) can beimplemented in assembly or machine language, if desired. In any case,the language may be a compiled or interpreted language, and combinedwith hardware implementations.

The methods and apparatus of the present invention may also be practicedvia communications embodied in the form of program code that istransmitted over some transmission medium, such as over electricalwiring or cabling, through fiber optics, or via any other form oftransmission, wherein, when the program code is received and loaded intoand executed by a machine, such as an EPROM, a gate array, aprogrammable logic device (PLD), a client computer, a video recorder orthe like, or a receiving machine having the signal processingcapabilities as described in exemplary embodiments above becomes anapparatus for practicing the invention. When implemented on ageneral-purpose processor, the program code combines with the processorto provide a unique apparatus that operates to invoke the functionalityof the present invention. Additionally, any storage techniques used inconnection with the present invention may invariably be a combination ofhardware and software.

While the present invention has been described in connection with thepreferred embodiments of the various figures, it is to be understoodthat other similar embodiments may be used or modifications andadditions may be made to the described embodiment for performing thesame function of the present invention without deviating therefrom. Forexample, while exemplary network environments of the invention aredescribed in the context of a networked environment, such as a peer topeer networked environment, one skilled in the art will recognize thatthe present invention is not limited thereto, and that the methods, asdescribed in the present application may apply to any computing deviceor environment, such as a gaming console, handheld computer, portablecomputer, etc., whether wired or wireless, and may be applied to anynumber of such computing devices connected via a communications network,and interacting across the network. Furthermore, it should be emphasizedthat a variety of computer platforms, including handheld deviceoperating systems and other application specific operating systems arecontemplated, especially as the number of wireless networked devicescontinues to proliferate. Still further, the present invention may beimplemented in or across a plurality of processing chips or devices, andstorage may similarly be effected across a plurality of devices.Therefore, the present invention should not be limited to any singleembodiment, but rather should be construed in breadth and scope inaccordance with the appended claims.

1. A method for selecting output attributes for use in a decision tree from a set of possible output attributes comprising: determining an interestingness score for each output attribute based on the difference between the entropy of the output attribute E(A) and a most favored entropy value m; and selecting at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores.
 2. A method according to claim 1, where said determination of an interestingness score for each output attribute comprises: determining an interestingness score equivalent to −(m−E(A))².
 3. A method according to claim 1, where said most favored entropy value m is set by the user.
 4. A method according to claim 1, where said most favorite entropy value m is dynamically chosen while performing said method.
 5. A method according to claim 1, where said selection of at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores comprises: selecting the K output attributes with the highest interestingness scores for use in said decision trees.
 6. A method according to claim 5, where said selection of at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores further comprises: sorting the output attributes by interestingness score.
 7. A method according to claim 5, where the value of K is set by the user.
 8. A method according to claim 5, where the value of K is dynamically chosen while performing said method.
 9. A method according to claim 1, where said selection of at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores comprises: selecting the output attributes with interestingness score greater than a minimum interestingness value for use in said decision tree.
 10. A method according to claim 9, where the value of said minimum interestingness value is set by the user.
 11. A method according to claim 9, where the value of said minimum interestingness value is dynamically chosen while performing said method.
 12. A method for selecting output attributes for use in a decision tree from a set of possible output attributes and for selecting input attributes for use in said decision tree from a set of possible input attributes comprising: determining an interestingness score for each output attribute based on the difference between the entropy of the output attribute E(A) and a most favored entropy value m; selecting at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores; determining a score gain sum for each input attribute based on the sum of gain scores over all of said selected at least one output attribute for use in said decision tree; and selecting at least one input attribute for use in said decision tree from said set of possible input attributes based on said score gain sums.
 13. A method according to claim 12, where said determination of an interestingness score for each output attribute comprises: determining an interestingness score equivalent to −(m−E(A))².
 14. A method according to claim 12, where said selection of at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores comprises: selecting the K output attributes with the highest interestingness scores for use in said decision trees.
 15. A method according to claim 12, where said selection of at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores comprises: selecting the output attributes with interestingness score greater than a minimum interestingness value for use in said decision tree.
 16. A method according to claim 12, where gain score of an input attribute over an output attribute is equal to the split score of said input attribute and said output attribute minus the node score of said input attribute over the training data.
 17. A method according to claim 12, where said selection of at least one input attribute for use in said decision tree from said set of possible input attributes based on said score gain sums comprises: selecting the J output attributes with the highest score gain sums for use in said decision trees.
 18. A method according to claim 17, where said selection of at least one input attribute for use in said decision tree from said set of possible input attributes based on said interestingness scores comprises: sorting the input attributes by score gain sum.
 19. A method according to claim 17, where the value of J is set by the user.
 20. A method according to claim 17, where the value of J is dynamically chosen while performing said method.
 21. A method according to claim 12, where said selection of at least one input attribute for use in said decision tree from said set of possible input attributes based on said interestingness scores comprises: selecting the input attributes with score gain sums greater than a minimum score gain sum for use in said decision tree.
 22. A method according to claim 21, where the value of said minimum score gain sum is set by the user.
 23. A method according to claim 21, where the value of said minimum score gain sum is dynamically chosen while performing said method.
 24. A method for selecting input attributes for use in said decision tree from a set of possible input attributes comprising: determining a score gain sum for each input attribute based on the sum of gain scores over all output attributes for use in said decision tree; and selecting at least one input attribute for use in said decision tree from said set of possible input attributes based on said score gain sums.
 25. A method according to claim 24, where gain score of an input attribute over an output attribute is equal to the split score of said input attribute and said output attribute minus the node score of said input attribute over the training data.
 26. A method according to claim 24, where said selection of at least one input attribute for use in said decision tree from said set of possible input attributes based on said score gain sums comprises: selecting the J output attributes with the highest score gain sums for use in said decision trees.
 27. A method according to claim 26, where said selection of at least one input attribute for use in said decision tree from said set of possible input attributes based on said interestingness scores comprises: sorting the input attributes by score gain sum.
 28. A method according to claim 26, where the value of j is set by the user.
 29. A method according to claim 26, where the value of J is dynamically chosen while performing said method.
 30. A method according to claim 24, where said selection of at least one input attribute for use in said decision tree from said set of possible input attributes based on said interestingness scores comprises: selecting the input attributes with score gain sums greater than a minimum score gain sum for use in said decision tree.
 31. A method according to claim 30, where the value of said minimum score gain sum is set by the user.
 32. A method according to claim 30, where the value of said minimum score gain sum is dynamically chosen while performing said method.
 33. A computer-readable storage medium comprising computer-executable modules having computer-executable instructions for selecting output attributes for use in a decision tree from a set of possible output attributes and for selecting input attributes for use in said decision tree from a set of possible input attributes, said modules comprising: a module for determining an interestingness score for each output attribute based on the difference between the entropy of the output attribute E(A) and a most favored entropy value m; a module for selecting at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores; a module for determining a score gain sum for each input attribute based on the sum of gain scores over all of said selected at least one output attribute for use in said decision tree; and a module for selecting at least one input attribute for use in said decision tree from said set of possible input attributes based on said score gain sums.
 34. A computer-readable storage medium according to claim 33, where said module for determining an interestingness score for each output attribute comprises: a module for determining an interestingness score equivalent to −(m−E(A))².
 35. A computer-readable storage medium according to claim 33, where said module for selecting at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores comprises: a module for selecting the K output attributes with the highest interestingness scores for use in said decision trees.
 36. A computer-readable storage medium according to claim 33, where said module for selecting at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores comprises: a module for selecting the output attributes with interestingness score greater than a minimum interestingness value for use in said decision tree.
 37. A computer-readable storage medium according to claim 33, where gain score of an input attribute over an output attribute is equal to the split score of said input attribute and said output attribute minus the node score of said input attribute over the training data.
 38. A computer-readable storage medium according to claim 33, where said module for selecting at least one input attribute for use in said decision tree from said set of possible input attributes based on said score gain sums comprises: a module for selecting the J output attributes with the highest score gain sums for use in said decision trees.
 39. A computer-readable storage medium according to claim 33, where said module for selecting at least one input attribute for use in said decision tree from said set of possible input attributes based on said interestingness scores comprises: a module for selecting the input attributes with score gain sums greater than a minimum score gain sum for use in said decision tree.
 40. A computer device for selecting output attributes for use in a decision tree from a set of possible output attributes and for selecting input attributes for use in said decision tree from a set of possible input attributes, comprising: means for determining an interestingness score for each output attribute based on the difference between the entropy of the output attribute E(A,) and a most favored entropy value m; means for selecting at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores; means for determining a score gain sum for each input attribute based on the sum of gain scores over all of said selected at least one output attribute for use in said decision tree; and means for selecting at least one input attribute for use in said decision tree from said set of possible input attributes based on said score gain sums.
 41. A computer device according to claim 40, where said means for determining an interestingness score for each output attribute comprise: means for determining an interestingness score equivalent to −(m−E(A))².
 42. A computer device according to claim 40, where said means for selecting at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores comprise: means for selecting the K output attributes with the highest interestingness scores for use in said decision trees.
 43. A computer device according to claim 40, where said means for selecting at least one output attribute for use in said decision tree from said set of possible output attributes based on said interestingness scores comprise: means for selecting the output attributes with interestingness score greater than a minimum interestingness value for use in said decision tree.
 44. A computer device according to claim 40, where gain score of an input attribute over an output attribute is equal to the split score of said input attribute and said output attribute minus the node score of said input attribute over the training data.
 45. A computer device according to claim 40, where said means for selecting at least one input attribute for use in said decision tree from said set of possible input attributes based on said score gain sums comprise: means for selecting the J output attributes with the highest score gain sums for use in said decision trees.
 46. A computer device according to claim 40, where said means for selecting at least one input attribute for use in said decision tree from said set of possible input attributes based on said interestingness scores comprise: means for selecting the input attributes with score gain sums greater than a minimum score gain sum for use in said decision tree. 